Toss chicken breasts, limeade, and pepper in a bowl. Cook the chicken breasts in a skillet until no longer pink in the center and the juices run clear, about 8 minutes. Remove skillet from the heat and set aside.

Combine sugar, vinegar, salt, mustard, and onion in a blender. Process for about 20 seconds. With the blender on high speed, gradually add oil in a slow and steady stream. Stir in poppy seeds.

Arrange spinach on 4 salad plates and top with strawberries, peas, pecans, and the cooked chicken. Serve with the poppy seed dressing.